Putin is a paranoid coward and fears for his life like few people you know. No he's not going to "destroy the world", it would endanger his own life and the palaces he built for himself.
No it's not binary, there's a vast, vast gulf between limited nuclear use and a full-on attack on CONUS. In fact, any nuclear use by Russia would likely bring its rapid defeat, since their main allies (India and China) are nuclear armed countries with a border dispute and are very interested in the nuclear taboo staying intact.
No it's not "Mutually Assured Destruction", the mainstream of nuclear targeting is counter-force disarming strikes, and the US is perfectly capable of winning a nuclear war. "Winning" here means ending up in a situation where cities are mostly intact on both sides, but only one side is capable of threatening them. Moreover, being credibly capable of winning a nuclear exchange was (during the Cold War) and is necessary to keep European and Asian allies safe. No, militaries are not deliberately glassing cities if push comes to shove, it doesn't make any military or political sense. You don't kill a hostage to win a negotiation.
No, a nuclear war is not a "suicide". It's very bad news for everyone (although chances are we will see battlefield nuclear use in our lifetime), but there's an incredible amount of nuance and complexity. "Putin presses the red button and everyone's dead" is a take that is not even wrong.